Mean degree of ad hoc networks in environments with obstacles

In ad hoc networks, the mean degree represents the average number of neighbors per station. The larger this value, the better the connectivity of the network. A direct consequence for the stations is that, when the mean degree increases, exchanging information becomes easier. In this work we study the sensitivity of the mean degree according to the variation of several characteristics related to the obstacles and to the environment in which the stations are positioned in. For that purpose, we provide a new method based on a careful geometric analysis and we show that, under a restricted set of assumptions, the value of the mean degree can be computed using a generic formula whose parameters depend on the size of the environment and on few geometric characteristics of the obstacles.